# Extensions 1→N→G→Q→1 with N=2- 1+4 and Q=C22

Direct product G=N×Q with N=2- 1+4 and Q=C22
dρLabelID
C22×2- 1+464C2^2xES-(2,2)128,2324

Semidirect products G=N:Q with N=2- 1+4 and Q=C22
extensionφ:Q→Out NdρLabelID
2- 1+41C22 = C42.15D4φ: C22/C1C22 ⊆ Out 2- 1+4168+ES-(2,2):1C2^2128,934
2- 1+42C22 = D811D4φ: C22/C1C22 ⊆ Out 2- 1+4168+ES-(2,2):2C2^2128,2020
2- 1+43C22 = D8.13D4φ: C22/C1C22 ⊆ Out 2- 1+4328-ES-(2,2):3C2^2128,2021
2- 1+44C22 = D8○SD16φ: C22/C1C22 ⊆ Out 2- 1+4324ES-(2,2):4C2^2128,2022
2- 1+45C22 = C2×D4.8D4φ: C22/C2C2 ⊆ Out 2- 1+432ES-(2,2):5C2^2128,1748
2- 1+46C22 = C42.12C23φ: C22/C2C2 ⊆ Out 2- 1+4168+ES-(2,2):6C2^2128,1753
2- 1+47C22 = C2×D4○SD16φ: C22/C2C2 ⊆ Out 2- 1+432ES-(2,2):7C2^2128,2314
2- 1+48C22 = C2×Q8○D8φ: C22/C2C2 ⊆ Out 2- 1+464ES-(2,2):8C2^2128,2315
2- 1+49C22 = C8.C24φ: C22/C2C2 ⊆ Out 2- 1+4324ES-(2,2):9C2^2128,2316
2- 1+410C22 = D8⋊C23φ: C22/C2C2 ⊆ Out 2- 1+4168+ES-(2,2):10C2^2128,2317
2- 1+411C22 = C4.C25φ: C22/C2C2 ⊆ Out 2- 1+4328-ES-(2,2):11C2^2128,2318
2- 1+412C22 = C2×C2.C25φ: trivial image32ES-(2,2):12C2^2128,2325
2- 1+413C22 = 2+ 1+6φ: trivial image168+ES-(2,2):13C2^2128,2326
2- 1+414C22 = 2- 1+6φ: trivial image328-ES-(2,2):14C2^2128,2327

Non-split extensions G=N.Q with N=2- 1+4 and Q=C22
extensionφ:Q→Out NdρLabelID
2- 1+4.1C22 = C42.16D4φ: C22/C1C22 ⊆ Out 2- 1+4328-ES-(2,2).1C2^2128,935
2- 1+4.2C22 = C42.17D4φ: C22/C1C22 ⊆ Out 2- 1+4164ES-(2,2).2C2^2128,936
2- 1+4.3C22 = Q8≀C2φ: C22/C1C22 ⊆ Out 2- 1+4164-ES-(2,2).3C2^2128,937
2- 1+4.4C22 = D86D4φ: C22/C1C22 ⊆ Out 2- 1+4164ES-(2,2).4C2^2128,2023
2- 1+4.5C22 = D8○Q16φ: C22/C1C22 ⊆ Out 2- 1+4324-ES-(2,2).5C2^2128,2025
2- 1+4.6C22 = C2×D4.10D4φ: C22/C2C2 ⊆ Out 2- 1+432ES-(2,2).6C2^2128,1749
2- 1+4.7C22 = C42.313C23φ: C22/C2C2 ⊆ Out 2- 1+4164ES-(2,2).7C2^2128,1750
2- 1+4.8C22 = M4(2).C23φ: C22/C2C2 ⊆ Out 2- 1+4328-ES-(2,2).8C2^2128,1752
2- 1+4.9C22 = C42.13C23φ: C22/C2C2 ⊆ Out 2- 1+4328-ES-(2,2).9C2^2128,1754

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